The relevance of this paper is explained by a demand for the development of mechanical and mathematical models and methods for calculating the stress-strain state of the sandwich structural elements. The statement of the boundary value problem on the deformation of a circular sandwich plate with a central hole, connected to the soil foundation, was given. To describe the kinematics of an asymmetric plate pack, the broken line hypotheses are accepted. In a relatively thick lightweight core, the normal does not change its length, remains rectilinear, but rotates through some additional angle. Tuff, coarse grained soil, granite, and gneiss are accepted as the soil foundation. The bearing reaction is described by the Winkler model. The system of equilibrium equations is obtained by the variational method. Its solution is written in displacements through Kelvin functions. A numerical parametric analysis of displacements and stresses in the plate is carried out, their dependence on the type of soil foundation is shown.